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Accuracy of the Jacobi Method on Scaled Diagonally Dominant Symmetric Matrices

This paper proves that the two-sided Jacobi method computes the eigenvalues of the indefinite symmetric matrix to high relative accuracy, provided that the initial matrix is scaled diagonally dominant. It proves sharp eigenvalue perturbation bounds coming from a single Jacobi step and from the whole sweep defined by the serial pivot strategies.

symmetric matrices; eigenvalues; Jacobi method;

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